The behaviour of quasi-linear maps on $C(K)$-spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912913112956928 |
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| author | Sánchez, Félix Cabello Castillo, Jesús M. F. Salguero-Alarcón, Alberto |
| author_facet | Sánchez, Félix Cabello Castillo, Jesús M. F. Salguero-Alarcón, Alberto |
| contents | In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a $C(K)$ must be nontrivial on a subspace isomorphic to $c_0$. We conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of $\ell_1$ and $c_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The behaviour of quasi-linear maps on $C(K)$-spaces Sánchez, Félix Cabello Castillo, Jesús M. F. Salguero-Alarcón, Alberto Functional Analysis In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a $C(K)$ must be nontrivial on a subspace isomorphic to $c_0$. We conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of $\ell_1$ and $c_0$. |
| title | The behaviour of quasi-linear maps on $C(K)$-spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.17432 |